#include #include #include #include #include #include #include #include #include #include #include #include #define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl; #define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } using namespace std; typedef long long ll; double dpa[55][55][55][55]; double dpb[55][55][55][55]; double dpc[55][55][55][55]; bool ok[55][55][55][55]; double cb2(int x){ return (x*(x-1))/2; } void calc(int a, int b, int c, int n){ if(a+b+c <= 1) return; if(n == 0) return; if(ok[a][b][c][n]) return; double pa = (cb2(a)/cb2(a+b+c)); double pb = (cb2(b)/cb2(a+b+c)); double pc = (cb2(c)/cb2(a+b+c)); if(a > 1){ calc(a-1, b, c, n-1); dpa[a][b][c][n] += pa+dpa[a-1][b][c][n-1]*pa; dpb[a][b][c][n] += dpb[a-1][b][c][n-1]*pa; dpc[a][b][c][n] += dpc[a-1][b][c][n-1]*pa; } if(b > 1){ calc(a, b-1, c, n-1); dpa[a][b][c][n] += dpa[a][b-1][c][n-1]*pb; dpb[a][b][c][n] += pb+dpb[a][b-1][c][n-1]*pb; dpc[a][b][c][n] += dpc[a][b-1][c][n-1]*pb; } if(c > 1){ calc(a, b, c-1, n-1); dpa[a][b][c][n] += dpa[a][b][c-1][n-1]*pc; dpb[a][b][c][n] += dpb[a][b][c-1][n-1]*pc; dpc[a][b][c][n] += pc+dpc[a][b][c-1][n-1]*pc; } calc(a, b, c, n-1); double p = 1.0-(pa+pb+pc); dpa[a][b][c][n] += dpa[a][b][c][n-1]*p; dpb[a][b][c][n] += dpb[a][b][c][n-1]*p; dpc[a][b][c][n] += dpc[a][b][c][n-1]*p; ok[a][b][c][n] = true; } int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; int a, b, c, n; cin >> a >> b >> c >> n; calc(a, b, c, n); cout << dpa[a][b][c][n] << ' ' << dpb[a][b][c][n] << ' ' << dpc[a][b][c][n] << endl; }